Question

1. a collection of nickels and quarters has a total value of three dollars and contains 32 coins. which of the following systems of equations could be used to find the number of each coin?

〇 $n + q = 32$ and $.05n +.25q = 300$
〇 $n + q = 32$ and $.05n +.25q = 3.00$
〇 $n + q = 32$ and $.5n +.25q = 3.00$
〇 $n + q = 32$ and $5n + 25q = 3$

Explanation:

Step1: Define variables

Let $N$ = number of nickels, $Q$ = number of quarters.

Step2: Set total coin count equation

Total coins = 32, so $N + Q = 32$.

Step3: Set total value equation

A nickel = $0.05$, a quarter = $0.25$, total value = $3.00$. So $0.05N + 0.25Q = 3.00$.

Step4: Match to options

Compare the two equations to the given choices.

Answer:

B. $N + Q = 32$ and $.05N + .25Q = 3.00$